TSTP Solution File: QUA011^1 by Leo-III-SAT---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : QUA011^1 : TPTP v8.2.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 02:30:29 EDT 2024
% Result : Theorem 18.98s 4.36s
% Output : Refutation 19.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 16
% Syntax : Number of formulae : 57 ( 39 unt; 9 typ; 3 def)
% Number of atoms : 107 ( 74 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 191 ( 22 ~; 9 |; 16 &; 144 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 38 ( 38 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 82 ( 35 ^ 31 !; 16 ?; 82 :)
% Comments :
%------------------------------------------------------------------------------
thf(emptyset_type,type,
emptyset: $i > $o ).
thf(emptyset_def,definition,
( emptyset
= ( ^ [A: $i] : $false ) ) ).
thf(singleton_type,type,
singleton: $i > $i > $o ).
thf(singleton_def,definition,
( singleton
= ( ^ [A: $i,B: $i] : ( B = A ) ) ) ).
thf(zero_type,type,
zero: $i ).
thf(sup_type,type,
sup: ( $i > $o ) > $i ).
thf(multiplication_type,type,
multiplication: $i > $i > $i ).
thf(crossmult_type,type,
crossmult: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(crossmult_def,definition,
( crossmult
= ( ^ [A: $i > $o,B: $i > $o,C: $i] :
? [D: $i,E: $i] :
( ( A @ D )
& ( B @ E )
& ( C
= ( multiplication @ D @ E ) ) ) ) ) ).
thf(sk1_type,type,
sk1: $i > $o ).
thf(sk16_type,type,
sk16: $i ).
thf(sk18_type,type,
sk18: $i ).
thf(4,axiom,
! [A: $i] :
( ( sup @ ( singleton @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sup_singleset) ).
thf(15,plain,
! [A: $i] :
( ( sup
@ ^ [B: $i] : ( B = A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(16,plain,
! [A: $i] :
( ( sup
@ ^ [B: $i] : ( B = A ) )
= A ),
inference(cnf,[status(esa)],[15]) ).
thf(17,plain,
! [A: $i] :
( ( sup
@ ^ [B: $i] : ( B = A ) )
= A ),
inference(lifteq,[status(thm)],[16]) ).
thf(3,axiom,
( ( sup @ emptyset )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sup_es) ).
thf(13,plain,
( ( sup
@ ^ [A: $i] : $false )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(14,plain,
( ( sup
@ ^ [A: $i] : $false )
= zero ),
inference(lifteq,[status(thm)],[13]) ).
thf(39,plain,
! [A: $i] :
( ( A = zero )
| ( ( sup
@ ^ [B: $i] : ( B = A ) )
!= ( sup
@ ^ [B: $i] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[17,14]) ).
thf(43,plain,
! [A: $i] :
( ( A = zero )
| ( ( ^ [B: $i] : ( B = A ) )
!= ( ^ [B: $i] : $false ) ) ),
inference(simp,[status(thm)],[39]) ).
thf(7,axiom,
! [A: $i > $o,B: $i > $o] :
( ( multiplication @ ( sup @ A ) @ ( sup @ B ) )
= ( sup @ ( crossmult @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplication_def) ).
thf(24,plain,
! [A: $i > $o,B: $i > $o] :
( ( multiplication @ ( sup @ A ) @ ( sup @ B ) )
= ( sup
@ ^ [C: $i] :
? [D: $i,E: $i] :
( ( A @ D )
& ( B @ E )
& ( C
= ( multiplication @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(25,plain,
! [B: $i > $o,A: $i > $o] :
( ( multiplication @ ( sup @ A ) @ ( sup @ B ) )
= ( sup
@ ^ [C: $i] :
? [D: $i,E: $i] :
( ( A @ D )
& ( B @ E )
& ( C
= ( multiplication @ D @ E ) ) ) ) ),
inference(cnf,[status(esa)],[24]) ).
thf(26,plain,
! [B: $i > $o,A: $i > $o] :
( ( multiplication @ ( sup @ A ) @ ( sup @ B ) )
= ( sup
@ ^ [C: $i] :
? [D: $i,E: $i] :
( ( A @ D )
& ( B @ E )
& ( C
= ( multiplication @ D @ E ) ) ) ) ),
inference(lifteq,[status(thm)],[25]) ).
thf(270,plain,
! [B: $i > $o,A: $i > $o] :
( ( ( multiplication @ zero @ ( sup @ B ) )
= ( sup
@ ^ [C: $i] :
? [D: $i,E: $i] :
( ( A @ D )
& ( B @ E )
& ( C
= ( multiplication @ D @ E ) ) ) ) )
| ( ( sup
@ ^ [C: $i] : $false )
!= ( sup @ A ) ) ),
inference(paramod_ordered,[status(thm)],[14,26]) ).
thf(271,plain,
! [A: $i > $o] :
( ( multiplication @ zero @ ( sup @ A ) )
= ( sup
@ ^ [B: $i] :
? [C: $i,D: $i] :
( $false
& ( A @ D )
& ( B
= ( multiplication @ C @ D ) ) ) ) ),
inference(pattern_uni,[status(thm)],[270:[bind(A,$thf( ^ [C: $i] : $false ))]]) ).
thf(341,plain,
! [A: $i > $o] :
( ( multiplication @ zero @ ( sup @ A ) )
= ( sup
@ ^ [B: $i] : $false ) ),
inference(simp,[status(thm)],[271]) ).
thf(352,plain,
! [A: $i > $o] :
( ( multiplication @ zero @ ( sup @ A ) )
= zero ),
inference(rewrite,[status(thm)],[341,14]) ).
thf(353,plain,
! [A: $i > $o] :
( ( ( multiplication @ zero @ zero )
= zero )
| ( ( sup
@ ^ [B: $i] : $false )
!= ( sup @ A ) ) ),
inference(paramod_ordered,[status(thm)],[14,352]) ).
thf(354,plain,
( ( multiplication @ zero @ zero )
= zero ),
inference(pattern_uni,[status(thm)],[353:[bind(A,$thf( ^ [B: $i] : $false ))]]) ).
thf(1,conjecture,
! [A: $i > $o] :
( ( multiplication @ ( sup @ A ) @ zero )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplication_anni) ).
thf(2,negated_conjecture,
~ ! [A: $i > $o] :
( ( multiplication @ ( sup @ A ) @ zero )
= zero ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(10,plain,
~ ! [A: $i > $o] :
( ( multiplication @ ( sup @ A ) @ zero )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,plain,
( ( multiplication @ ( sup @ sk1 ) @ zero )
!= zero ),
inference(cnf,[status(esa)],[10]) ).
thf(12,plain,
( ( multiplication @ ( sup @ sk1 ) @ zero )
!= zero ),
inference(lifteq,[status(thm)],[11]) ).
thf(395,plain,
( ( multiplication @ ( sup @ sk1 ) @ zero )
!= ( multiplication @ zero @ zero ) ),
inference(paramod_ordered,[status(thm)],[354,12]) ).
thf(409,plain,
( ( ( sup @ sk1 )
!= zero )
| ( zero != zero ) ),
inference(simp,[status(thm)],[395]) ).
thf(414,plain,
( ( sup @ sk1 )
!= zero ),
inference(simp,[status(thm)],[409]) ).
thf(613,plain,
! [A: $i] :
( ( ( ^ [B: $i] : ( B = A ) )
!= ( ^ [B: $i] : $false ) )
| ( A
!= ( sup @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[43,414]) ).
thf(614,plain,
( ( ^ [A: $i] :
( A
= ( sup @ sk1 ) ) )
!= ( ^ [A: $i] : $false ) ),
inference(pattern_uni,[status(thm)],[613:[bind(A,$thf( sup @ sk1 ))]]) ).
thf(714,plain,
( sk16
= ( sup @ sk1 ) ),
inference(func_ext,[status(esa)],[614]) ).
thf(723,plain,
( ( sup @ sk1 )
= sk16 ),
inference(lifteq,[status(thm)],[714]) ).
thf(272,plain,
! [B: $i > $o,A: $i > $o] :
( ( ( multiplication @ ( sup @ A ) @ zero )
= ( sup
@ ^ [C: $i] :
? [D: $i,E: $i] :
( ( A @ D )
& ( B @ E )
& ( C
= ( multiplication @ D @ E ) ) ) ) )
| ( ( sup
@ ^ [C: $i] : $false )
!= ( sup @ B ) ) ),
inference(paramod_ordered,[status(thm)],[14,26]) ).
thf(273,plain,
! [A: $i > $o] :
( ( multiplication @ ( sup @ A ) @ zero )
= ( sup
@ ^ [B: $i] :
? [C: $i,D: $i] :
( ( A @ C )
& $false
& ( B
= ( multiplication @ C @ D ) ) ) ) ),
inference(pattern_uni,[status(thm)],[272:[bind(A,$thf( A )),bind(B,$thf( ^ [C: $i] : $false ))]]) ).
thf(342,plain,
! [A: $i > $o] :
( ( multiplication @ ( sup @ A ) @ zero )
= ( sup
@ ^ [B: $i] : $false ) ),
inference(simp,[status(thm)],[273]) ).
thf(1261,plain,
! [A: $i > $o] :
( ( multiplication @ ( sup @ A ) @ zero )
= zero ),
inference(rewrite,[status(thm)],[342,14]) ).
thf(1299,plain,
! [A: $i > $o] :
( ( ( multiplication @ sk16 @ zero )
= zero )
| ( ( sup @ sk1 )
!= ( sup @ A ) ) ),
inference(paramod_ordered,[status(thm)],[723,1261]) ).
thf(1300,plain,
( ( multiplication @ sk16 @ zero )
= zero ),
inference(pattern_uni,[status(thm)],[1299:[bind(A,$thf( sk1 ))]]) ).
thf(731,plain,
( ( multiplication @ sk16 @ zero )
!= zero ),
inference(rewrite,[status(thm)],[12,723]) ).
thf(846,plain,
! [A: $i] :
( ( ( ^ [B: $i] : ( B = A ) )
!= ( ^ [B: $i] : $false ) )
| ( A
!= ( multiplication @ sk16 @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[43,731]) ).
thf(847,plain,
( ( ^ [A: $i] :
( A
= ( multiplication @ sk16 @ zero ) ) )
!= ( ^ [A: $i] : $false ) ),
inference(pattern_uni,[status(thm)],[846:[bind(A,$thf( multiplication @ sk16 @ zero ))]]) ).
thf(889,plain,
( sk18
= ( multiplication @ sk16 @ zero ) ),
inference(func_ext,[status(esa)],[847]) ).
thf(905,plain,
( ( multiplication @ sk16 @ zero )
= sk18 ),
inference(lifteq,[status(thm)],[889]) ).
thf(1325,plain,
sk18 = zero,
inference(rewrite,[status(thm)],[1300,905]) ).
thf(924,plain,
sk18 != zero,
inference(rewrite,[status(thm)],[731,905]) ).
thf(1326,plain,
$false,
inference(simplifyReflect,[status(thm)],[1325,924]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : QUA011^1 : TPTP v8.2.0. Released v4.1.0.
% 0.12/0.16 % Command : run_Leo-III %s %d
% 0.17/0.38 % Computer : n002.cluster.edu
% 0.17/0.38 % Model : x86_64 x86_64
% 0.17/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38 % Memory : 8042.1875MB
% 0.17/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38 % CPULimit : 300
% 0.17/0.38 % WCLimit : 300
% 0.17/0.38 % DateTime : Mon May 20 13:39:39 EDT 2024
% 0.17/0.38 % CPUTime :
% 1.07/0.95 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.44/1.09 % [INFO] Parsing done (137ms).
% 1.44/1.10 % [INFO] Running in sequential loop mode.
% 1.80/1.38 % [INFO] nitpick registered as external prover.
% 1.80/1.38 % [INFO] Scanning for conjecture ...
% 1.94/1.46 % [INFO] Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ...
% 2.19/1.48 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 2.19/1.49 % [INFO] Problem is higher-order (TPTP THF).
% 2.19/1.49 % [INFO] Type checking passed.
% 2.19/1.49 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 18.98/4.35 % [INFO] Killing All external provers ...
% 18.98/4.35 % Time passed: 3813ms (effective reasoning time: 3251ms)
% 18.98/4.35 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 18.98/4.36 % Axioms used in derivation (3): sup_singleset, sup_es, multiplication_def
% 18.98/4.36 % No. of inferences in proof: 45
% 18.98/4.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3813 ms resp. 3251 ms w/o parsing
% 19.07/4.44 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 19.07/4.44 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------